Does the sensor size matters in the size and weight of an equivalent lens? Why?

In other words, does the size of projected image circle matters in the size and weight of two lenses with the same aperture/DOF (different f-number) and field of view (different mm)? All other things equal, will a 40mm F4 full-frame lens be identical in dimensions and weight to a 20mm F2 Micro 4/3 lens? Or bigger? Or smaller? Why?

Does the f-number matters in that answer? Like, a 40mm F5.6 is the same size of a 20mm F2.8 but a 40mm F2.8 is smaller than a 40mm F1.4? I ask because a moderator here called jrista stated the following in a answer to the question Does the size of the front glass mean anything? :

once you pass f/2.8, each additional stop greatly increases the physical size of the lens. Additionally, once you pass f/2.8, each additional stop requires a considerably greater amount of light, and larger front lens elements are a key factor in gathering that additional light.

But I don't understand why F2.8 is such a "magical" turning point.

As a side question, the design of both lenses has to be totally different? Or is it just a matter of changing one or two glass elements at the base of the lens to adjust the projected image size? I ask that because one can transform a 40mm F4 lens into almost a 20mm F2 lens with a speed booster, but there are many downsides to that as it is extra glass. But if the manufacturer can make such minimal changes on the lenses avoiding those downsides, why I have never seen they release two versions of the same lens at the same time, one for APS-C and another for full-frame, like they do for different mounts?